I. Field of the Invention
The present invention relates to signal compression. More particularly, the present invention relates to a novel and improved method and apparatus for compressing a fixed point signal without introducing a bias.
II. Description of the Related Art
Electronic digital systems often represent numbers internally according to two different formats: floating point and fixed point. Floating point notation has no fixed decimal point. Numbers are represented in floating point by two components: a mantissa and an exponent. Fixed point, on the other hand, is a format in which all numerical quantities are expressed by a predetermined number of digits, with the decimal point implicitly located at some predetermined position. Fixed point numbers are the subject of the current invention.
Systems designers endeavor to represent numbers with as few bits as possible. The expense and complexity of hardware depends, in part, on the number of bits: the more bits, the larger and more complex the hardware. Saving even a single bit translates into a direct reduction in hardware costs. Designers determine the system's dynamic range requirements and set the number of bits accordingly.
Different signals within a digital system may have different dynamic range requirements. For instance, multiplication of an M-bit number with and N-bit number results in a product having M+N bits for full precision. However, the system may not require that the product signal have that high a dynamic range. It may, therefore, be desirable to discard bits from the signal (i.e., compress the signal).
Two conventional approaches to signal compression are truncation and rounding. Truncation refers to simply dropping one or more of the least significant bits or digits in this case from a signal. Truncation, however, introduces a negative bias into the compressed signal because truncation always involves throwing away a positive quantity (the truncated bits). These biases accumulate as more truncation operations are performed. This accumulated bias can significantly degrade downstream performance, particularly in low signal level environments. Rounding performs better than truncation, but nevertheless introduces a bias that also can degrade downstream performance.
Thus, there exists a need for a method and apparatus designed to compress fixed point signals without introducing a bias.